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arXiv · hep-th/0612154

Exact classical solutions of nonlinear sigma models on supermanifolds

Ryu Sasaki·Wen-Li Yang·Yao-Zhong Zhang
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Abstract

We study two-dimensional nonlinear sigma models with target spaces being the complex super Grassmannian manifolds, that is, coset supermanifolds $G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for $0\leq p \leq m$, $0\leq q \leq n$ and $1\leq p+q$. The projective superspace ${\bf CP}^{m-1|n}$ is a special case of $p=1$, $q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm-Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super case published more than twenty years ago by one of the present authors.

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Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang. 2007-03-15. Exact classical solutions of nonlinear sigma models on supermanifolds. https://doi.org/10.1016/j.nuclphysb.2007.03.013

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